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    SURFACE ESTIMATION BASED ON LIDAR

    Wolfgang Schickler

    Anthony Thorpe

    Sanborn

    1935 Jamboree Drive, Suite 100

    Colorado Springs, CO 80920

    [email protected]

    [email protected]

    Abstract

    In the past several years, the use of airborne laser systems or LIDAR for the rapid collection of digital terrainmodels (DTMs) has proliferated. Flood plain studies, contouring, road engineering projects, volumetric

    computations, ortho-photo production, and mapping for beach erosion are just some of the applications driving the

    demand for this technology. The ability of LIDAR systems to capture accurate spot heights at an extremely rapid

    rate is the principle reason behind LIDAR's success.

    Many applications, for example, contouring, require a bald-earth DTM. Unfortunately, the raw data pointscaptured by LIDAR do not constitute a bald-earth DTM. Even though most LIDAR systems can measure "last-

    return" data points, these "last-return" points often measure ground clutter like shrubbery, cars, buildings, and even

    the canopy of dense foliage. Consequently, raw LIDAR points must be post-processed to remove these undesirablereturns. The degree to which this post processing is successful is critical in determining whether LIDAR is cost

    effective for large-scale mapping applications.

    We present our approach to estimating bald-earth surfaces from LIDAR data. Our approach is different from

    typical approaches in that we estimate a surface based on the original LIDAR points while at the same time

    considering important supplementary information. This other information includes independently measured break-

    lines and surface categories. We use a least-squares adjustment with robust estimation similar to that proposed by(Kraus, Pfeifer, 1998). The surface model is represented using a triangular irregular network or TIN. We present

    examples from a real mapping project that demonstrate the success of this approach.

    Introduction

    LIDAR systems have become one of the prime methods for rapid collection of large-scale height data for

    various applications, especially in Europe where LIDAR is used for creating and updating national DTMs.

    Although LIDAR technology is widely used by mapping companies, the reliable, efficient creation of accurateDTMs from LIDAR measurements is problematic. (Huising, Gomes, 1998) identify two major problems: the

    elimination of systematic errors and the selection of ground points, i.e. the derivation of a bald-earth DTM from

    LIDAR measurements.

    The presence of systematic errors can often be observed between overlapping LIDAR strips. The modeling and

    elimination of these systematic errors is currently a topic of research (Burman, 2000). The second problem is the

    derivation of a bald-earth DTM from LIDAR measurements. LIDAR pulses measure not only on the ground but also

    ground clutter like shrubbery, cars, buildings, and tree canopies. Consequently, raw LIDAR points must be post-processed to remove these undesirable returns.

    In this paper we paper we focus on the second problem, the derivation of a bald-earth DTM from LIDARmeasurements.

    Previous Work

    Several publications deal with the problem of bald-earth DTM derivation from LIDAR measurements. Almost

    all of them either use one of the following two approaches or a combination of both. The first approach is a filtering

    Published in: Proceedings of the ASPRS Annual Conference. St. Louis, Missouri, April 2001.

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    method that is either based on mathematical morphology or based on the analysis of structural information like

    slope. The second approach is a surface estimation method that is usually based on least squares interpolation.

    (Lindenberger, 1993) adopts the filtering approach and uses a morphological filter to eliminate non-ground

    points. He applies an opening to the LIDAR data using a horizontal structural element. This is followed by an auto-

    regressive process to improve the results. (Kilian et al, 1996) also use a morphological filter. They then perform aweighted smoothing of the surface based on the distance of the individual LIDAR points to the opened surface. They

    conclude that the size of the structural element used for the opening is a critical parameter for which there is nosingle optimal value. They suggest the usage of multiple openings with different sizes of structural elements.

    (Vosselman, 2000) presents an approach for LIDAR data filtering that is closely related to a morphological

    filter. He estimates an optimal filter function by analyzing the height differences between ground points in trainingdata sets. He shows that his slope-based filtering is superior to a morphological filter with a horizontal structural

    element.

    (Kraus, Pfeifer, 1998) describe an approach for DTM estimation based on a robust, finite-element estimation fordata with an asymmetrical error distribution. Our approach is an extension of this work and is described in more

    detail later.

    There are several commercial packages available for the post processing of LIDAR measurements. The

    (Optech, 2001) LIDAR system comes with a post-processing package. The algorithm used for the filtering is not

    published. The parameter set for the algorithm and the artifacts observed in the processed data suggest that the

    algorithm is based on a morphological filter. (TerraSolid, 2001) offers a variety of LIDAR processing modules,including TerraScan for the filtering and thinning of LIDAR data. This package includes different methods for

    slope-based filtering and thinning of LIDAR data. (INPHO GmbH, 2001) offers a product called SCOP for the

    derivation of DTMs and contours from various sources, including LIDAR data. The approach for the LIDAR dataprocessing is based on the method described in (Kraus, Pfeifer, 1998).

    Overview of Our Approach

    We call our approach FASE for Filtering And Surface Estimation. It is based on the estimation technique

    proposed by (Kraus, Pfeifer, 1998). We favor this approach because it yields a direct estimate of the ground surface

    without a prior process of filtering. In other words, vegetation and other ground-clutter measured by the LIDAR are

    removed implicitly during the estimation process. This provides greater control of the results because allinformation is available to the surface estimator, which can make a "more informed" estimate of the ground surface.

    Our approach differs from (Kraus, Pfeifer, 1998) in the following ways. First, our surface model is a

    triangulation and not a rectangular grid. Second, we include independently measured mass-points and break-lines in

    the estimation with appropriate weighting. Third, we add additional curvature constraints and slope constraints tocontrol the shape of the estimated surface. Fourth, we employ the concept of surface classes to guide the estimation

    process. These features are described in more detail in the next section.

    Surface Estimation

    The next sub-sections give a brief introduction in the (Kraus, Pfeifer, 1998) approach for surface estimation in

    wooded areas. We introduce our extensions and describe our functional model in more detail.

    Review of the Kraus approach

    The (Kraus, Pfeifer, 1998) approach for surface estimation is based on a robust finite element estimation fordata with an asymmetrical error distribution. A conventional robust estimation iteratively de-weights observationswith large residuals according to the weight function shown as a dashed line in Figure 1. (Kraus, Pfeifer, 1998)

    propose a decentralized, one-sided weight function as shown as a solid line in Figure 2. This one-sided weight

    function only de-weights observations with large positive residuals. It favors LIDAR points that are on the ground

    by lowering the weights of points on trees or other vegetation.

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    They propose a one-sided weight function to

    compute the weights P as a function of normalized

    residuals, nr. It has the following form.

    1 : nr < g

    P(nr) =

    1 / ( 1 + ( a( nr g) )2

    : nr g

    They suggest changing the parameters of the weight

    function, especially the parameter defining the origin g

    and the shape or the aggressiveness a, based on thelocal distribution of the LIDAR data. (Pfeifer, et.al,

    1998) describe an adaptive method to accomplish this, which uses a histogram analysis.

    Surface ModelWe use a surface model based on a Delaunay

    triangulation and not a rectangular grid. The elevation

    of each node in the triangular grid is considered an

    unknown and is estimated by the process. The main

    advantage of this model over the rectangular grid is that

    it adapts easily to varying point densities. That is, asparse point distribution can be used in flat areas or in

    areas where the LIDAR data are scarce. Conversely,

    where the terrain is broken or where the LIDAR dataare dense, the node spacing in the triangulation can be

    tightened to better estimate surface detail.

    For mapping products like large-scale contouring,

    our experience shows that the LIDAR data must oftenbe supplemented with break-lines and mass-points.

    LIDAR data sometimes is not dense enough toaccurately model sharp surface discontinuities. In

    addition, dense undergrowth near small streams, forexample, prevents the LIDAR pulses from penetrating

    to the true ground surface. Our use of a triangulated

    surface model allows us to elegantly include externally

    measured break-lines and mass-points into theestimation process.

    The surface model is constructed as follows. A triangulation is constructed from any available mass-points andbreak-lines. Then, a regularly spaced grid of points is added to the triangulation. These grid points are generated

    such that equilateral triangles are produced in the triangulation. Elevations for every node in the triangulation are

    estimated as described in the next section. Note that elevations for the mass-points and break-lines are re-estimatedtoo. In doing so, the estimation algorithm takes into account the relative accuracy of the LIDAR points and the

    externally measured break-lines and mass-points. Figure 2 shows an example of our surface model based on an

    equilateral triangulation of grid points plus additional break-lines. Note that although supplementary break-lines and

    mass-points help to define the surface, our approach does not depend on them. Typically, break-lines and mass-points are only used for high-accuracy products like large-scale contouring. In the case of contouring, break-lines

    can improve the appearance of contours, for example, near road edges.

    Figure 1 One-sided robust weight function

    (solid) and robust weight function (dashed).

    Figure 2: Surface model based on anequilateral Delaunay triangulation with added

    break-lines.

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    Functional Model

    The height of each node in the triangulation is represented by an unknown in a robust estimation. The functionalmodel for the surface estimation is based on the following four different types of observations:

    1. Each LIDAR point constitutes one observation equation. The functional relation between the LIDAR point andthe unknown triangulation points is based on the Hessian normal form for a planar surface.

    2. Slope constraints are applied to the each edge of the triangulation. Each observation equation is based on theslope (first derivative) of the edge. The expected value of the slope is assumed to be zero.3. Curvature constraints are applied to each edge in the triangulation that is common to two triangles. Each

    observation equation is based on a numerical estimate of the second derivative across the edge. The expected

    value of the curvature is assumed to be zero. No curvature constraints are added to edges belonging to a break-

    line.

    4. Break-line points and mass-points are introduced in a Bayesian manner as direct observations of the unknowns.An equation system is constructed from the above observations. The least-squares solution to the system uses a

    weight matrix that is derived from the a-priori variances of the observations. These weights are normalized by area.In accordance with robust estimation theory, the weights for the LIDAR point observations are iteratively

    recomputed based on normalized residuals and the previously described weight functions.

    We can tune the input parameters, for example the constraint weights or the a priori variances of the LIDARpoints, to achieve smooth, rugged, flat, or horizontal surfaces. This is similar to an approach for surface estimation

    based on matched image points implemented in MATCH-T and described in (Wild, et al, 1996).

    Surface Classes

    Motivation. Others, for example Vosselman (2000), suggest having multiple parameter settings, which are applied

    depending on the morphological characteristics of the terrain. This is a central concept in our approach: we make

    use of surface classes to assist the estimation process. Input parameters that define the functional and stochasticmodel of the estimation process have a profound influence on the resulting surface. We use surface classification

    information like forest areas, building outlines, or water bodies to select different parameter sets. We use the term

    "surface class" to describe the pairing of each type of surface classification with a corresponding parameter set.

    In addition, a LIDAR project area will also include many different surface types: different kinds of forests with

    leaf-on or leaf-off conditions, open grassland, rivers, lakes, and urban areas with buildings and individual trees. Indense trees, the penetration rate of the LIDAR pulses to the ground may be less than 20%. Water bodies can causespecula reflections, which can result in no water level measurements. In urban areas, the LIDAR returns will

    measure miscellaneous ground clutter like cars, bushes, and buildings. In other words, the distribution of recordedLIDAR points is significantly different for each of these surface areas. Consequently, using a fixed parameter set

    for an entire project area will yield a result that is a compromise. Parameters chosen to optimize surface estimation

    in trees will give an overly generalized surface in open areas. This is additional motivation for the use of surface

    classes.

    Parameter sets. We have identified four parameters, which significantly impact the shape of the estimated

    surface. The four parameters we use to model the different surface classes are listed below.

    1. The standard deviation of the individual LIDAR points have a direct impact on how close the estimated surfacefits these observations (the smaller the standard deviation, the larger the impact of the individual observation).

    2. The standard deviation of the curvature constraint affects the smoothness or stiffness of the surface. Stiffersurfaces also tend to discard LIDAR points with large positive residuals, e.g., returns from trees.

    3. The standard deviation of the slope constraint defines the levelness of the surface. Smaller standarddeviations lead to surfaces that are closer to horizontal. This is useful for modeling water bodies.

    4. The parameters of the one-sided robust estimation function control the aggressiveness of the weight function.A more aggressive weight function will favor low points more and high points less.

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    We call the collection of the above parameters a parameter set. Different parameter sets can be chosen to

    perform optimal estimation in areas of forest, buildings, or water bodies. Our task is to efficiently choose where to

    apply each parameter set.

    Surface regions. We associate different parameter sets with classified regions of the project surface, and we

    call the resulting association a surface class. Sources for the classified regions include existing GIS data layers,classified hyper-spectral imagery, or photogrammetrically captured polygon boundaries like building outlines. One

    of our goals is to use the LIDAR data directly to derive some of the surface classes. We have had some successusing both the first and last returns to automatically classify tree areas.

    Automatic building extraction from LIDAR data is currently a research topic. Several promising approaches

    have been presented to automatically extract the 3-D structure of buildings. Examples are (Brunn, Weidner, 1998)and (Maas, 1999). For the surface regions, we only need the 2-D outlines of buildings. This simpler problem might

    be solved by creating a triangulation of LIDAR points and looking for close-to-vertical slopes.

    Implementation. We have implemented our surface classes using inheritance. That is, a sub-class inherits aparameter from its super-class, unless the sub-class overrides the parameter. This allows us to easily define, for

    example, a tree super-class with leaf-on and leaf-off sub-classes. The table below shows six examples of surface

    classes, each with a qualitative definition of the four parameters we use to control the surface.

    LIDAR point

    weightSlope Constraint Curvature Constraint

    Aggressiveness of

    weight function

    Trees leaf-off Moderate Turned off Moderate High

    Trees leaf-on Moderate Turned off High High

    Buildings Very low Turned off High Normal

    Lake Normal Very high High High

    River Normal High High High

    Open Space Normal Turned off Normal Normal

    Examples

    We present examples for two different small areas in Gwinnett County, Georgia. The LIDAR data were

    captured from a nominal elevation of 1200m AGL with a nominal point spacing of 2.5m. The data were captured aspart of an update-mapping project.

    Example Area #1

    The first area contains several large buildings in an office park. Figure 3 shows an orthophoto of the area

    overlaid with the planimetric data used for surface regions and for break-lines. Break-lines are shown in yellow andbuilding outlines are shown in red. We show the results for three different DTM extraction techniques in figures 4-

    9. These techniques are raw data (no filtering), slope-based filtering (TerraSolid), and FASE. Figures 4-6 show the

    contours from the DTM extracted with each technique, and figures 7-9 show perspectives of each DTM. The same

    set of break lines was used to generate contours for the filtered data and FASE data.

    We note the following:

    1. The raw data is not useful for a bald-earth DTM as it contains buildings. Notice the presence of significantsurface noise caused by the overlap of two LIDAR strips (figures 4 and 7). This example was chosen for its

    abnormally high elevation bias between the two LIDAR strips, in this case, approximately 30cm.

    2. The contours derived from the filtered data set (figure 5) have many undesirable isolations and depressions.3. The filtering algorithm, by itself, was unable to remove the largest building. Changing the filtering parameters

    could help but would introduce undesirable effects elsewhere.

    4. The FASE output (figures 6 and 9) shows smooth contours with all buildings removed.

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    Example Area #2

    The second example is a residential area that contains two lakes, a forested area, and several medium-sizedbuildings. Figure 10 shows an orthophoto image of the area overlaid with the planimetric data used for surface

    regions and for break-lines. Break-lines are shown in yellow, lakes in blue, building outlines in red, and forest

    outlines in green. We show the results for the three different DTM extraction techniques in figures 11-16. Figures

    11-13 show the contours from the DTM extracted with each technique, and figures 14-16 show perspectives of each

    DTM. The same set of break lines was used to generate contours for the filtered data and FASE data.

    We note the following:

    1. The raw data is not useful for a bald-earth DTM as it contains buildings and trees. Note also the contourproblems in lakes due to overhanging trees (figure 11).

    2. The contours derived from the filtered data set (figure 12) have many undesirable isolations and depressions. Inour opinion, they have too much character.

    3. Note also in figure 12 that the drainage break-line from the lake "digs" below the LIDAR data. This causes theundesirable contour artifacts along the break-line.

    4. The filtered data set does not model the lakes properly.5. The FASE output (figures 13 and 16) shows that the lakes have been correctly modeled, buildings have been

    removed, vegetation is removed, and break-lines have been incorporated.

    Discussion

    The estimation technique that we employ eliminates many of the problems seen with filtering and point

    classification techniques. We assert that estimating a new surface has an advantage over methods that pick and

    choose points from an data set in which individual points have errors. Hill cut-off problems (morphological filtering)and oddly spaced point clusters (slope based filter) are not present in our results.

    Using surface estimation rather than filtering to extract digital terrain models (DTM) also has the benefit ofsmoothing noise in the LIDAR data. When two strips of LIDAR data overlap, they will not match exactly. Even if

    the elevation bias between the two strips is only 10cm, the combined point surface will be noisy. Contours

    generated from these points appear choppy and aesthetically unpleasing. When a new surface is estimated throughthese noisy points, the result is a smoother surface that represents the average of the points. This surface is most

    likely more accurate as well.

    Our use of surface classes provides a critical benefit. By guiding the surface estimation process with surface

    classes, we are able to reliably remove ground clutter like vegetation and buildings, an extremely important function.

    Water bodies can also be forced to be flat.

    When coupled with a stereo workstation, FASE is a powerful editing tool for LIDAR data. Stereo operators canconcentrate on helping the estimation process with supplementary break-lines and mass-points instead of performing

    bulk edits on huge quantities of raw LIDAR points. Stereo operators can also look directly at contours. They need

    not be bothered with the performance degradation and display saturation associated with displaying 150,000 LIDARpoints in a stereo model.

    One drawback to our approach is the computational effort. The computational time for this surface estimationexceeds that required for a morphological or slope-based filter. In our tests, the computational time required for a

    large-scale stereo-model was 10 minutes. This cost must be weighed against the benefits to determine whether the

    benefits of the surface estimation technique are justified. Certain LIDAR applications, like surface models forsmall-scale ortho-photography, probably don't require this technique.

    Our approach is not limited to the estimation of a bald earth surface. Modifying the one-sided weight function

    so that high points are favored over low points allows estimating a canopy surface that follows the top of trees and

    buildings from last-return LIDAR data. This may be useful for Telecom applications that require surfaces for line-

    of-sight analysis.

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    Conclusion

    We have described an approach to estimating bald-earth surfaces from LIDAR data. Our approach, called

    FASE, is based on a surface estimation technique supplemented with additional information in the form of break-

    lines, mass-points, and surface classes. The examples we show demonstrate the success of this approach and itspotential to automate the extraction of high-quality digital terrain models from LIDAR data.

    We will concentrate future research to developing better classifiers for vegetation and buildings. In essence, ourgoal is to develop an automated method of detecting buildings and vegetation areas directly from the LIDAR data.

    Information like return intensity and first-and-last returns will be helpful in this regard.

    Acknowledgments

    The imagery and LIDAR data used in the examples are owned by Gwinnett County. We thank them for

    permission to use the data for this publication.

    We give credit to Martin Huber from Munich University who developed the first prototype of FASE during an

    Internship program at ASI.

    References:

    Brunn, A., Weidner, U., (1998). Hierarchical Bayesian Nets for Building Extraction Using Dense Digital SurfaceModels,ISPRS Journal for Photogrammetry & Remote Sensing, Vol. 53, No.6, 1998, pp. 296-307 .

    Burman. H., (2000). Adjustment of Laser Scanner Data for Correction of Orientation Errors,International Archives

    of Photogrammetry and Remote Sensing, Vol. XXXIII, Part B3, Amsterdam 2000, pp. 125-132.

    Huising, E. J., Gomes Pereira, L. M., (1998). Errors and accuracy estimates of laser data acquired by various laser

    scanning systems for topographic applications,ISPRS Journal of Photogrammetry and Remote Sensing, Vol 53, No.

    5, 1998, pp. 254-261.

    INPHO GmbH, (2001). URL: http://www.inpho.de/ visited Jan. 2001.

    Kilian, J., Haala, N., Englich, M., (1996). Capture and evaluation of airborne laser scanner data, InternationalArchives of Photogrammetry and Remote Sensing, Vol. XXXII, Part B3, Vienna pp. 383-388.

    Kraus, K., Pfeifer, N., (1998) Determination of terrain models in wooded areas with airborne laser scanner data,

    ISPRS Journal of Photogrammetry & Remote Sensing, Vol. 53, 1998.

    Maas, H.-G., (1999). Fast determination of parametric house models from dense airborne laser scanner data.IAPRS,

    Vol. 32, Part 2W1, 5W1, IC5/3W, Bangkok, Thailand, 1999.

    Optech, (2001). URL: http://optech.on.ca/visited Jan. 2001.

    Pfeifer, N., Koestli, A., Kraus K., (1998). Interpolation of Laser Scanner Data Implementation and First Results,International Archives of Photogrammetry and Remote Sensing, Vol. XXXII, Part 3/1, Columbus, pp. 153-159.

    TerraSolid, (2001). URL: http://terrasolid.fi/TScan.htmvisited Jan 2001.

    Vosselmann, G., (2000). Slope Based Filtering of Laser Altimetry Data,International Archives of Photogrammetry

    and Remote Sensing, Vol. XXXIII Part B3, Amsterdam 2000, pp. 935-942.

    Wild, D., Krzystek, P., Madani, M., (1996). Automatic Breakline Detection using an Edge Preserving Filter,

    International Archives of Photogrammetry and Remote Sensing, Vol. XXXII, Part B3, Vienna 1996.

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    Figure 3: Orthophoto image overlaid with planimetric

    data for example area #1.

    Figure 4: Contours derived from the raw LIDAR

    surface.

    Figure 5: Contours derived from filtered LIDAR surface

    and supplementary break-lines.

    Figure 6: Contours derived from the FASE surface and

    supplemental break-lines.

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    Figure 7: Perspective view of raw LIDAR surface

    Figure 8: Perspective view of filtered LIDAR surface and supplementary break-lines.

    Figure 9: Perspective view of FASE surface.

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    Figure 10: Orthophoto image overlaid with planimetric

    data for example area #2.

    Figure 11: Contours derived from the raw LIDAR

    surface.

    Figure 12: Contours derived from filtered LIDAR

    surface and supplementary break-lines.

    Figure 13: Contours derived from FASE surface and

    supplementary break-lines.

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    Figure 14: Perspective view of raw LIDAR surface.

    Figure 15: Perspective view of filtered LIDAR surface and supplementary break-lines.

    Figure 16: Perspective view of FASE surface.